Preemptive Scheduling of Parallel Jobs on Multiprocessors

Deng, Xiaotie; Gu, Nian; Brecht, Tim; Lu, KaiCheng

doi:10.1137/s0097539797315598

Cited by 31 publications

(56 citation statements)

References 13 publications

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“…Other previous works on parallel jobs (see, e.g., [1] and [3]) assume an even partition of the processing of a job J j among machines that run J j in parallel, while we do not use this assumption (see Section 2.1).…”

Section: Related Workmentioning

confidence: 99%

Minimizing Makespan and Preemption Costs on a System of Uniform Machines

Shachnai

Tamir

Woeginger

2002

Algorithms — ESA 2002

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Abstract. It is well known that for preemptive scheduling on uniform machines there exist polynomial time exact algorithms, whereas for non-preemptive scheduling there are probably no such algorithms. However, it is not clear how many preemptions (in total, or per job) suffice in order to guarantee an optimal polynomial time algorithm. In this paper we investigate exactly this hardness gap, formalized as two variants of the classic preemptive scheduling problem.In generalized multiprocessor scheduling (GMS) we have a job-wise or total bound on the number of preemptions throughout a feasible schedule. We need to find a schedule that satisfies the preemption constraints, such that the maximum job completion time is minimized. In minimum preemptions scheduling (MPS) the only feasible schedules are preemptive schedules with the smallest possible makespan. The goal is to find a feasible schedule that minimizes the overall number of preemptions. Both problems are NP-hard, even for two machines and zero preemptions.For GMS, we develop polynomial time approximation schemes, distinguishing between the cases where the number of machines is fixed, or given as part of the input. Our scheme for a fixed number of machines has linear running time, and can be applied also for instances where jobs have release dates, and for instances with arbitrary preemption costs. For MPS, we derive matching lower and upper bounds on the number of preemptions required by any optimal schedule. Our results for MPS hold for any instance in which a job, J j , can be processed simultaneously by ρ j machines, for some ρ j ≥ 1.

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Section: Related Workmentioning

confidence: 99%

Minimizing Makespan and Preemption Costs on a System of Uniform Machines

Shachnai

Tamir

Woeginger

2002

Algorithms — ESA 2002

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“…GRAD achieves O(1)-competitiveness with respect to makespan for job sets with arbitrary release times, and O(1)-competitiveness with respect to mean response time for batched job sets where all jobs are released simultaneously. Unlike many previous results, which either assume clairvoyance [29,21,31] or use instantaneous parallelism [10,6], GRAD removes these restrictive assumptions. Moreover, because the quantum length can be adjusted to amortize the cost of context-switching during processor reallocation, GRAD provides effective control over the scheduling overhead and ensures efficient utilization of processors.…”

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confidence: 94%

Provably-Efficient Online Adaptive Scheduling of Parallel Jobs Based on Simple Greedy Rules

He¹,

Hsu²

2008

Greedy Algorithms

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“…The scheduling of a collection of parallel jobs onto a multiprocessor is an old and well-studied topic of research [15,17,18,22,31,36,39,50,53,54]. In this paper, we study so-called space-sharing [25] for parallel jobs, where jobs occupy disjoint processor resources, as opposed to time-sharing [25], where different jobs may share the same processor resources at different times.…”

Section: Introductionmentioning

confidence: 99%

“…The question of how the job scheduler should partition the multiprocessor among the various jobs has been studied extensively [17,18,22,23,31,36,38,39,41,46,47,55], but the administrative policy of the job scheduler is not the focus of this paper. Instead, we study the problem of how the task scheduler provides effective parallelism feedback to the job scheduler without knowing the future progress of the job, the future availability of processors, or the administrative priorities of the job scheduler.…”

Section: Introductionmentioning

confidence: 99%

“…Various researchers [17,18,31,39,55] have used the notion of instantaneous parallelism, 1 the number of processors the job can effectively use at the current moment, as the parallelism feedback to the job scheduler. Although using instantaneous parallelism for parallelism feedback is simple, it can cause gross misallocation of processor resources [48].…”

Section: Introductionmentioning

confidence: 99%

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Adaptive Scheduling with Parallelism Feedback

Agrawal

Hsu

et al. 2007

2007 IEEE International Parallel and Distributed Processing Symposium

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Multiprocessor scheduling in a shared multiprogramming environment is often structured as two-level scheduling, where a kernellevel job scheduler allots processors to jobs and a user-level task scheduler schedules the work of a job on the allotted processors. In this context, the number of processors allotted to a particular job may vary during the job's execution, and the task scheduler must adapt to these changes in processor resources. For overall system efficiency, the task scheduler should also provide parallelism feedback to the job scheduler to avoid the situation where a job is allotted processors that it cannot use productively.We present an adaptive task scheduler for multitasked jobs with dependencies that provides continual parallelism feedback to the job scheduler in the form of requests for processors. Our scheduler guarantees that a job completes near optimally while utilizing at least a constant fraction of the allotted processor cycles. Our scheduler can be applied to schedule data-parallel programs, such as those written in High Performance Fortran (HPF), *Lisp, C*, NESL, and ZPL.Our analysis models the job scheduler as the task scheduler's adversary, challenging the task scheduler to be robust to the system environment and the job scheduler's administrative policies. For example, the job scheduler can make available a huge number of processors exactly when the job has little use for them. To analyze the performance of our adaptive task scheduler under this stringent adversarial assumption, we introduce a new technique called "trim analysis," which allows us to prove that our task scheduler performs poorly on at most a small number of time steps, exhibiting nearoptimal behavior on the vast majority.To be precise, suppose that a job has work T1 and critical-path length T∞ and is running on a machine with P processors. Using trim analysis, we prove that our scheduler completes the job in O(T1/ P + T∞ + L lg P ) time steps, where L is the length of a scheduling quantum and P denotes the O(T∞ + L lg P )-trimmed availability. This quantity is the average of the processor availabilThis research was supported in part by the Singapore-MIT Alliance and NSF Grant ACI-0324974. Yuxiong He is a Visiting Scholar at MIT CSAIL and a Ph.D. candidate at the National University of Singapore. Wen Jing Hsu is a Visiting Scientist at MIT CSAIL and Associate Professor at Nanyang Technological University.Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. ity over all time steps excluding the O(T∞ + L lg P ) time steps with the highest processor availability. When T1/T∞ P (the job's parallelism dominates the O(T∞ + L lg P )-trimmed availability), the job ach...

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Preemptive Scheduling of Parallel Jobs on Multiprocessors

Cited by 31 publications

References 13 publications

Minimizing Makespan and Preemption Costs on a System of Uniform Machines

Minimizing Makespan and Preemption Costs on a System of Uniform Machines

Provably-Efficient Online Adaptive Scheduling of Parallel Jobs Based on Simple Greedy Rules

Adaptive Scheduling with Parallelism Feedback

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